"THERMOELASTIC DISPLACEMENT DUE TO TRANSIENT SURFACE HEATING "

Abstract

The starting point in the calculation of normal displacement due to transient heating is the Green’s function for the elastic half-space. Superposition principle leads to a triple integral (double integral over surface and simple integral over time) that can be formally re-written as a three-dimensional convolution product. Given the singularities of the Green’s function in the time/space domain, it is more convenient to employ its spectral counterpart, i.e. the frequency response function (FRF), in the convolution calculation. A special technique for the calculation of the 3D convolution product based on the FRF is advanced in this paper. The resulting algorithm is very efficient from a computational point of view, as the transfers to and from the time/space domain to the frequency domain are handled by the fast Fourier transform. A simulation example is presented, involving the transient thermoelastic displacement due to a uniform heat source that vanishes everywhere except for a square surface domain, and which is applied continuously only in a limited time window. The numerical results predict that the displacement increases with time as long as heat is supplied, and is gradually recovered once the heat is removed. The loaded half-space patch undergoes a growth-release process that is accurately captured by the simulation method. The developed framework anticipates the solution of the contact process with transient heating.